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<TITLE>Computer Algebra </TITLE> <P>
<H2>Computer Algebra - Richard Zippel</H2>
<HR>

<H2> Research Summary</H2>

Currently, my activities in computer algebra fall into three different
areas.  We are continuing to develop a very flexible computer algebra
substrate called Weyl, which extends Common Lisp to have symbolic
computing facilities.  This substrate has a functorial architecture
that has been implemented using object oriented programming
techniques.  The functorial organization allows one to define
algebraic structures over arbitrary algebraic domains.  This approach
permits algebraic structures like groups, rings and fields to be first
class objects that can be manipulated by the user.
<P>
We have been attempting to link together Weyl with Bob's Constable's
theorem proving system, Nuprl.  This will allow us state and use
theorem about algebraic structures when deciding which algorithms
should be used Weyl.
<P>
In additon, I have been continuing my work on algorithms in computer
algebra.  Among the problems I have been studying include: algebraic
function decomposition (with Dexter Kozen and Susan Landau) and
primality testing of polynomials.

<HR>

<H2> Publications </H2>
<UL>
<LI> <I> Effective Polynomial Computation</I>, Kluwer Academic Publishers, 
1993. 
<P>
<LI> "A New Modular Interpolation Algorithm for Factoring Multivariate 
Polynomials", (with Ronitt Rubinfeld), 1993.
<A HREF=http://cs-tr.cs.cornell.edu/TR/CORNELLCS:TR93-1326?abstract=>Cornell Computer Science Technical Report.</A>
<P>
<LI> "Rational Function Decomposition",
<I> Proceedings of the International Symposium on Symbolic
and Algebraic Computation</I>, Bonn, Germany, July 1991.
(<A HREF=http://cs-tr.cs.cornell.edu/TR/CORNELLCS:TR91-1209?abstract=>Tech Report</A>)
<P>
<LI> "Weyl Computer Algebra Substrate", 
<I>Design and Implementation of Symbolic Computation Systems '93</I>,
Springer-Verlag Lecture Notes in Computer Science 722, pp. 303-318.
(<A HREF=http://cs-tr.cs.cornell.edu/TR/CORNELLCS:TR90-1077?abstract=>Tech Report</A>)
<P>
<LI> "Interpolating polynomials from their values,"
<I> Journal of Symbolic Computation</I>, vol. 9, 1990, 375-403.
(<A HREF=http://cs-tr.cs.cornell.edu/TR/CORNELLCS:TR89-963?abstract=>Tech Report</A>)
<P>
<LI> "An Explicit Separation of Relativised Random Polynomial Time and
Relativized Deterministic Polynomial Time," 
<I> Information Processing Letters</I>, vol. 33, 4, 1989, pp. 207-212.
(<A HREF=http://cs-tr.cs.cornell.edu/TR/CORNELLCS:TR89-965?abstract=>Tech Report</A>)
<P>
<LI> "Polynomial Decomposition Algorithms," (with David Barton),
<I> Journal of Symbolic Computation</I>, vol. 1, 2, 1985, 159-168.
<P>
<LI> "Simplification of expressions involving radicals,"
<I> Journal of Symbolic Computation</I>, vol. 1, 2, 1985, 189-210.
<P>
<LI> "An Extension of Liouville's Theorem," (with Joel Moses), 
<I>Proceedings of EUROSAM 79</I>, Springer-Verlag, Lecture Notes in Computer
Science 72, 1979.
</UL>
